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Pólya-Based Approximation for the ATM-Forward Implied Volatility

International Journal of Financial Engineering, Forthcoming

12 Pages Posted: 5 Apr 2017 Last revised: 16 Aug 2017

Ivan Matic

CUNY Baruch College

Rados Radoicic

Baruch College, City University of New York

Dan Stefanica

Baruch College, City University of New York

Date Written: April 3, 2017

Abstract

We introduce a closed form approximation for the implied volatility of ATM-forward options. The relative error of this approximation is uniformly bounded for all option maturities and implied volatilities. The approximation is extremely precise, having relative error less than 10−6 for all options with integrated volatility less than 1.9, such as options with maturity less than three years and implied volatility less than 100%. Moreover, the approximate implied volatilities fall within the implied volatility bid-ask spread for all the liquid options, such as options with volatility less than 200% and maturity less than nine years.

Keywords: Implied Volatility, Black-Scholes Model, ATM-Forward Options

JEL Classification: C60, C63

Suggested Citation

Matic, Ivan and Radoicic, Rados and Stefanica, Dan, Pólya-Based Approximation for the ATM-Forward Implied Volatility (April 3, 2017). International Journal of Financial Engineering, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2945646

Ivan Matic

CUNY Baruch College ( email )

17 Lexington Avenue
New York, NY 10021
United States

Rados Radoicic

Baruch College, City University of New York ( email )

17 Lexington Avenue
New York, NY 10021
United States

Dan Stefanica (Contact Author)

Baruch College, City University of New York ( email )

One Bernard Baruch Way
New York, NY 10010
United States

HOME PAGE: http://mfe.baruch.cuny.edu/dan-stefanica

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